Reciprocating oil pumps are traditionally operated by a beam pumping unit, as illustrated in FIG. 1 and described below, with a sinusoidal characteristic of reciprocating motion of a polished rod as dictated by the fixed speed of an electrical or gas prime mover and the geometry of the beam pumping unit. Conventionally, a constant crank speed is employed in the operation of the beam pumping unit; as a result, the geometry of the beam pumping unit dictates a rod speed which follows a curve which is sinusoidal in nature. Other types of pumping units, such as long stroke or hydraulically actuated pumping units, operate at a first constant speed of the polished rod during upstroke motion and at a second constant speed during down-stroke motion, with additional speed variability only during change of the direction of the motion. Some of the pumping units utilize variable control of prime movers to allow for easier change in fixed speed of the prime mover or the ability to choose variable speed of the prime mover in any desired portion of the pumping cycle.
A conventional sucker rod pumping system comprises surface equipment (the beam pumping unit, or pump jack), and downhole equipment (the sucker rod and pump) which operates in a well bore drilled into an oil reservoir. The interaction of the movable and stationary elements of the well and dynamic interaction with fluids present in the well creates a complicated mechanical system that requires precise design and control to be able to work in an efficient way.
In order to increase oil production, analysis and optimization of all of the elements of the sucker rod pumping system must be performed. The design of the oil well system equipment is usually performed on the basis of mechanical laws and special methods, and certain established analytical standards are required to enable development of a beneficial design and desired operation of the oil well. Such an analysis generally involves:                1. A dynamic analysis of the sucker rod system when the dynamic forces and stresses acting on the sucker rod are calculated (dynamic wave equation);        2. a kinetic analysis of the surface equipment (pumping unit);        3. analysis of the performance of the bottom-hole pump (well evaluation software); and        4. analysis of the performance of the oil reservoir (inflow performance relation).        
Such a system analysis presented in the prior art can provide correct and useful information on the original design of the well and on its performance, but only for the constant speed of the prime mover. Past attempts to increase well production have incorporated changing the components of the rod string and size of the pump, changing the overall rotational velocity of the crank, varying the speed within the stroke by choosing different constant crank speeds for upstroke and clown-stroke with a variable frequency drive, or by utilizing ultra high slip electric motors to slow down speed of the prime mover during peak torque periods within a single stroke. Prior art has taught allowing for speed change of the prime mover as a response to the need for controlling pump-off conditions (U.S. Pat. Nos. 4,490,094; 4,973,226; and 5,252,031; please note that U.S. Pat. No. 5,252,031 is based on calculation of the down-hole pump behaviour as originally presented in U.S. Pat. No. 3,343,409), limiting loads on the rod string connecting surface unit with reciprocating pump and other components (U.S. Pat. Nos. 4,102,394 and 5,246,076; PCT Application No. WO 03/048578), optimizing pumping conditions of the pumping unit (U.S. Pat. Nos. 4,102,394 and 4,490,094), or converting the sinusoidal speed characteristic of the polished rod powered by a beam pumping unit to a linear characteristic throughout most of the upstroke and down-stroke motion (U.S. Pat. No. 6,890,156) to mimic long stroke behaviour with a typical pump-jack unit.
Most of the prior art methods and systems are based on various analyses of loads or energy on the polished rod and indirect detection of various problems with pump performance or fluid inflow to the well. U.S. Pat. No. 4,102,394, for example, teaches setting a different constant speed for the prime mover during upstroke movement as opposed to down-stroke movement to match inflow of the oil from the reservoir and to avoid pump-off conditions. The method of U.S. Pat. No. 4,490,094 determines and modifies the instantaneous speed of the prime mover for a predetermined portion of the polished rod stroke, based on power output and work done by the prime, mover. PCT Application No. WO 03/048578 teaches the application of finite changes to the speed of the prime mover within one stroke, to limit the load acting on the polished rod within pre-established safe limits. U.S. Pat. No. 6,890,156 teaches finite changes to the speed of the prime mover so the speed of the polished rod reciprocated by the beam pumping unit remains constant for an extended period during upstroke and down-stroke periods. Speed changes are dictated by the geometry of the beam pumping unit and are resulting in shorter stroke time for the same maximum speed of the polished rod. No relation or effect on the effective stroke of the pump or impact on maximum or minimum force acting in the rod string is taken into consideration or intentionally changed.
For over a decade, various suppliers of variable frequency drives (VFD) for beam pumping provided an opportunity to change the speed of the crank and polished rod within a single stroke of the pump. Some of the drives, such as the ePAC Vector Flux Drive from eProduction Solutions or the Sucker-Rod Pump Drive from Unico, Inc., allow a user to incorporate variable speed of the crank and rod throughout a single stroke by means of an incorporated Programmable Logic Controller and industry standard ladder programming language.
In the prior art, the speed of the polished rod was altered in order to improve, but not optimize, certain aspects of pump operations, such as reducing loads in the rod string, and their teachings had focused on the kinematics of the pumping system by prescribing certain movements of the polished rod without analyzing the dynamics of the entire system, including the surface unit, rod string and downhole pump. The optimization process was limited to the design phase, where, based on the system requirements and the dynamic analysis of the entire pumping system, the physical parameters of the system (such as motor power, rod string materials and dimensions, etc.) were determined to meet the required production target and satisfy the limits on the loads on the system. However, the optimization of the design assumed a constant speed of the prime mover.
While trying to improve the design of a new pumping system or improve the operation of an existing system, there was no attempt to optimize its performance by optimizing the stroke period and the variation of the prime mover speed within a stroke. Implementing such an approach creates an opportunity to develop a method and a system that can address the highly nonlinear nature of the problem of oil production optimization, while at the same time reducing operating costs and providing for operation with safe loading factors.